ADVANCED: Randomization

GVPT399F: Power, Politics, and Data

Randomization

  • Last session, we randomly assigned 1,000 hypothetical people to two different groups

  • Testing whether randomization helps us create two roughly identical groups prior to treatment

  • You now have a lot of the R code needed to replicate that analysis

Creating our group of 1,000 people

Imagine we have a group of 1,000 individuals. We know the following about them:

  • Height

  • Weight

  • Eye colour

Creating our group of 1,000 people

group_df <- tibble(
  id = 1:1000,
  height = rnorm(1000, 170, 6),
  weight = rnorm(1000, 80, 10),
  eye_colour = sample(c("Blue", "Green", "Brown", "Grey"), 
                      1000, 
                      replace = T)
)

group_df
# A tibble: 1,000 × 4
      id height weight eye_colour
   <int>  <dbl>  <dbl> <chr>     
 1     1   170.   76.5 Grey      
 2     2   167.   94.4 Grey      
 3     3   167.   83.0 Brown     
 4     4   175.   80.3 Blue      
 5     5   179.   58.4 Blue      
 6     6   185.   81.2 Brown     
 7     7   167.   77.6 Green     
 8     8   171.   74.0 Grey      
 9     9   169.   89.0 Brown     
10    10   177.  103.  Blue      
# ℹ 990 more rows

The Normal distribution

ggplot() + 
  geom_density(aes(x = rnorm(n = 1e6, mean = 0, sd = 1))) + 
  theme_minimal()

Random sampling from the Normal distribution

I can take a random sample of n values from a Normal distribution centered at some mean with a specific standard deviation.

  • By default, rnorm() takes a mean of 0 and a standard deviation of 1

  • The following code takes 1,000 random samples from that default Normal distribution

Random sampling from the Normal distribution

rnorm(n = 1000, mean = 0, sd = 1)
   [1]  0.0048649083  1.5214807345  0.7428227614  2.6231915530  0.0422385949
   [6]  1.3603462603  0.8416497109 -0.1344797685 -0.0609482260  0.3047704240
  [11]  0.0626695669 -1.0812897617 -0.0520075020 -0.1266255807 -0.2918669600
  [16] -0.6935976278 -0.3015969385  1.5774541057 -0.2862807808 -1.0954778440
  [21] -1.0250857023  1.5950175518  0.4083451163  0.8245344401  1.0852044913
  [26] -0.4418610031 -1.4588182941 -0.6327149491  0.5434635259  1.4665862707
  [31]  0.0539594675 -0.1340762606 -0.6532695988  0.6180425359  1.2129116736
  [36]  0.0080871961  0.6517970340  0.0947997216  0.9054258164  0.3220346145
  [41]  0.1192852685 -1.4008317184 -0.3733341862  0.0242761534  0.3765719317
  [46] -0.2898817897 -0.1007565775  0.8488142180  0.9193778983  1.3532338640
  [51] -0.1781288902  1.0662271558 -1.0052921146 -1.7213798199  1.2147933577
  [56] -0.2444856619  0.5284210026 -0.9865816151 -0.8875072934  0.5268250440
  [61]  0.0967908253 -1.3958731754 -0.9827613994  0.5312222436 -0.7833971629
  [66] -0.7169190016  1.3981124317 -0.2648730470 -0.3114032376 -0.2953388423
  [71] -1.7712677869  1.2086385225 -1.0633976370  0.8998404606 -0.0587209731
  [76]  1.1311583490 -0.0941478306  0.1811637698  0.0380626017 -0.3802560607
  [81]  0.8263447628 -0.7761590384  0.4705229362  1.7155630584 -0.3364888017
  [86]  0.8334324019  1.1610539122  0.6927481803 -0.3717974657 -1.6466530025
  [91]  0.3233691711 -1.9651185657 -0.5926512270 -1.1098081588 -1.4510954399
  [96] -1.2572175337  0.0670943838 -0.2119517591 -1.4567120017 -1.8294042668
 [101] -0.1054104198  1.0609441425 -0.3668203119  3.1422070590  0.4197923935
 [106] -0.5451493347 -0.4503616656  0.2989164168  0.2234648081  0.6230885061
 [111] -0.6739266513 -1.0683634578  1.3300834988  0.2830658593 -1.7523228541
 [116]  1.4171454069 -0.6779527455 -0.1527181668  0.8667363406 -0.4433095606
 [121]  0.7289242475  1.1118423980 -1.8790496729 -1.2088676990  0.4939471542
 [126]  0.3082657706  0.1529639344 -0.5596123646 -0.0235791372  0.1183642460
 [131]  0.8136047865  0.4128133619 -0.0983937213 -1.5071830245  3.2905581046
 [136]  0.1902858205  2.0252827652  0.0218410895  0.5085577404  0.7453612547
 [141]  0.9513176633  0.1922584029  0.5208999709 -0.2046540228 -1.7800234255
 [146] -1.1961206315  0.2492375265 -0.6662350231  1.1825706929 -1.1549478393
 [151] -0.9432503638 -0.7735475843  0.1062296141  0.6636037664  0.9003372904
 [156]  0.2421391484 -0.4207715409 -0.3123834729 -1.6030398866 -0.7976432460
 [161] -0.5221943894 -0.5219796237 -0.9598279197 -1.2532972268 -1.5579469820
 [166]  0.4823694861  2.1616593576  1.0382580204  1.8426008928  0.8935922850
 [171] -0.1625656109 -1.9564834804  0.4568431267  0.0499322056 -0.8105287804
 [176] -0.8453224903 -0.9300231049 -1.1889420097 -0.6279582512 -0.5762176095
 [181] -0.4486686126 -0.6018752836  1.0647686835  1.7714388610  0.7024676124
 [186] -0.6067199742 -1.9919832169 -0.1771535421 -0.0791855947 -0.2241329457
 [191]  0.6558616553  2.6412444787  1.9036663016  2.0090192133  0.1489735891
 [196]  0.2888187409 -1.4292288105 -0.6544058621  0.9411873290 -1.0917405403
 [201] -0.9915355443 -0.1007784948 -0.6717829229 -1.9723378662 -0.1099972200
 [206] -0.0409551292  0.3185966750  0.4417719703 -0.2866580260  0.1604976355
 [211]  0.0343786828 -0.3159808720 -0.0100434097 -1.2826453772 -0.3624620271
 [216]  1.2585357647  0.1077649120 -0.0975135167  0.9545541192  0.5866429244
 [221] -0.6045645751 -1.4338790755 -0.1055875728  0.8617273620  0.4699721788
 [226] -0.8782702638 -0.9622259539 -0.0785114966 -0.1913565144 -0.1048951685
 [231] -0.6469165730  0.7728042126 -2.2079265210 -0.0168364249 -0.9501923311
 [236] -0.5116715697  2.3281956205 -1.0574119061  1.0563291898  0.9819518748
 [241] -0.1659737552  0.2119666879 -0.7233376403 -0.1540697984  0.8698881864
 [246]  0.0851194261 -1.1319746321 -1.6060963540 -0.3982921535  0.7467136714
 [251] -0.8803928314  1.1740437308 -2.3289549947 -0.5862006706  1.0118875626
 [256] -0.1700856871  1.8250957975  0.4640789075  0.9282429619  0.1125979925
 [261]  2.0176359834 -0.5234007657  0.0054824255  0.5844287650 -1.9359622348
 [266] -0.1757217286  0.5855338061  0.6744638921 -0.1878109267  1.0957747014
 [271]  2.9156586355 -0.1909258021 -1.0739837635 -0.4893502680 -1.5810810812
 [276] -1.6726457766 -0.4089239843  1.0075511543  0.7062992955 -2.0669457038
 [281] -1.0437691869  0.2662796583 -0.9017698959  0.1937431976 -0.5825249744
 [286] -0.2142837307 -1.0558483619  0.6653337500  0.5496578822 -0.1273948627
 [291]  0.7311452125  1.1980684834 -0.2301263092 -0.6782892430  0.8858117405
 [296] -1.2209631987 -0.1710961862  0.8427883345  0.1034195555  0.1678577838
 [301] -0.9041328451 -0.0600853886  0.0374305075 -0.9133810569 -0.7297767194
 [306] -1.0082057639 -0.7992121629  0.7078654614  0.6913000287 -0.1877479140
 [311]  0.9792606423  0.1309313535 -0.2401937249  1.4610515734 -0.3894522613
 [316] -0.5158722067 -0.7348523492 -0.3568422666 -0.4373018524  0.6640257844
 [321] -0.7914927481 -0.7171039036  0.6095497789  0.1553310992 -0.9147868390
 [326]  1.0259842323  0.1181766362 -0.2385624881 -0.0757365330 -0.1805583296
 [331]  1.2661847219  1.2240400662  0.9496025507 -1.2437429692  0.6828937920
 [336]  0.1995174417  0.7584748642 -0.0072001350  1.5535831316 -0.0745116029
 [341] -1.1995525901 -1.5110629363  0.0021756893  0.8112250310  1.9850522120
 [346]  0.7712651434 -0.0863857955  0.7296744817 -0.2338149403 -0.2226625986
 [351] -0.8739232228 -0.4182262729 -0.1219489039 -0.5993784679  1.4261438871
 [356] -1.3235562338  0.6309444768  0.3076230757  1.3192932893  1.3255676256
 [361] -0.1517203323  0.3385011738  1.3018388503  0.2816913019  1.0480211638
 [366] -2.8907507846 -1.0096776409 -1.1254488350 -1.0466264691  0.2648675362
 [371] -0.1507001127  0.4497645474  1.0534760510 -0.7179857593  0.1023318060
 [376]  0.9496041648 -2.0851665399 -1.7428083972  0.6835094699  1.0564535960
 [381] -0.9966396747 -1.1151828987 -3.2466848535 -1.1308521375  1.0293754293
 [386]  1.8903177467  1.3344345297  0.7237551638  0.0096406544  0.2161306514
 [391]  1.6429305356 -0.7686786687  0.5051286241 -1.1102259585  0.9044517233
 [396]  0.9465359166  1.6426196659 -1.5552310971 -1.9943947343 -0.4054136156
 [401]  0.2104876833 -1.3545152077 -0.1044767398 -1.5332444590  1.6333324201
 [406] -0.8545329504 -0.2095782430  0.3580570745  1.7820562368 -0.2328405514
 [411]  0.2388950224 -1.8875371146  1.2305939073  1.4218707568  2.2901602811
 [416]  1.7511965545 -0.6341943765 -1.0277710701  1.5655927386 -0.9883588284
 [421]  0.5788069181 -0.3007657077 -0.4928509255 -1.2630184590 -0.1022361587
 [426] -0.2170256692  1.9883954561  0.1238527674 -0.5120772155 -0.3370555611
 [431] -0.0537970196 -0.0918330092 -0.9550449400 -0.2733770609  0.2547086496
 [436] -0.3947455006  0.4336768869  1.7467279552  0.2703303847  0.7319248425
 [441]  0.1626597362 -0.9845690283 -1.6257582813 -0.3264173960 -1.0834738833
 [446] -0.9469378476  0.3065087104  0.5065251559  0.0742563364 -0.0503739372
 [451] -0.4946577306 -1.4764146674  1.0390048292  0.1067511988 -0.1963327074
 [456]  0.5075203426  0.2530851213  1.0651864522 -1.6243240315 -0.2861673184
 [461] -0.8815937408 -2.5391278570 -0.1375731978  2.0183781737 -1.2450597776
 [466]  0.3283815834  0.0765666764  0.7726300827 -1.3446937164 -0.8718499701
 [471] -1.0985136816 -0.5402873157  0.9333469310 -0.2416512841  1.8047514425
 [476] -0.9983169075  0.1722751227 -0.2283854772  0.4757763337 -0.5361203684
 [481]  2.1343555549  1.2413638144  1.2013969087 -0.1271519929 -0.7812560002
 [486]  2.1239975948 -0.4192528028 -0.5377927831 -0.9624840287  0.4733710876
 [491]  0.6571622462 -0.6873521223 -0.1114255799 -0.8072284656 -1.7314977208
 [496]  2.4166731648 -0.2889139680 -0.7206686034 -2.1710532660  0.4448724334
 [501]  0.8252492351 -0.2007211418  1.1709196460 -0.8833848954  0.1783773256
 [506]  0.4368054587  0.3542148248 -1.1285688318 -0.3440905856 -2.3437182512
 [511]  0.3906045269 -0.8223045143  0.6645862573  1.6197410986  0.0445561319
 [516]  0.8231501781  1.8196713581 -0.7768216365  0.4981419165 -0.2589481357
 [521] -1.3852374972 -1.9654427150 -1.6438735596 -1.0618689328 -1.7795933752
 [526] -0.9329345046 -0.1190813140  0.5533926113 -0.2851669543  1.4495578991
 [531]  0.7909888005  0.4486676400  0.5817194247 -0.2498201532 -0.3718470120
 [536]  1.6210351410 -0.5500788440  1.4978674192 -0.3165716020 -0.5499997270
 [541] -0.0445015043  0.2297678602  1.7807200799 -0.6311822343  1.6260221290
 [546] -1.4715544685 -1.1111089738 -0.0477762653  0.5664750710 -0.6283447023
 [551] -0.3661997648 -0.4168839923  0.5084757418  1.3367052286 -0.8132313541
 [556]  0.6715464826  0.6037294558  1.4371682893 -0.2333038348 -1.0151321851
 [561] -0.2061068258  0.2267019127  1.0477909205 -0.3760774959  0.4649774643
 [566]  0.4338291253 -0.7249331017  1.5219959513  0.2208428382 -0.7540032218
 [571] -1.2459612654  0.6571128160 -1.7647459701  1.2474778521 -0.7978669663
 [576]  0.2629639294 -1.5716705825 -0.6218483218  0.4011163177 -1.3444547080
 [581]  1.5132137271 -0.0787303101 -1.3729723991 -0.7124350214  0.6367224411
 [586] -1.5513848894 -2.2800074353 -0.1374455089  0.3468318102  0.4853501890
 [591]  0.4196543150  0.6669257931  0.7941938554 -0.5585845453  0.0322147777
 [596]  0.3969921211 -0.1261122883 -0.2349355096 -1.2433651406  0.3669913199
 [601]  0.2374720428 -2.0560952140  0.3088787472 -0.4949568335 -0.0538509254
 [606] -0.2150676369 -0.3230254488  1.4870165861  1.1501163728  1.3072486118
 [611]  2.1080490371  0.6611744517  1.5163930014 -0.1398045052 -1.7517559751
 [616]  1.0852962076  1.6702288547 -0.9558543463  2.3502928967 -1.2937853746
 [621] -0.0804657879  0.0348156056  0.3764973292  1.4582162586 -1.0741004325
 [626] -0.1272767476 -1.3969810470  0.2463794006  1.0431344097 -0.3493578949
 [631]  0.0546856166  0.3273071776 -1.5058375456 -0.3492755675  0.4318567861
 [636] -0.1181174426  0.4125359288 -0.7687087012  0.9169163371 -1.7102067120
 [641] -0.9298603532 -1.1510662342 -0.6775450678  0.5621605256 -1.7256001595
 [646] -0.3957458784 -0.9962937650  0.0254891128 -1.1564635768  0.2630832439
 [651]  0.5549193959 -0.3737752422  0.6617650900 -0.1517028805 -1.7852066636
 [656] -0.2094738990 -1.2139523240 -0.9781524073 -0.4217498378 -0.1133036017
 [661]  0.2085919333 -0.2635321824 -0.7286357015  2.0614207257 -0.8474599585
 [666]  0.1755451372 -0.4444172448 -0.1303808276  0.8156708626  0.7202734732
 [671] -0.8898322090  0.0739213116  0.9954018733 -0.0635495408  0.4068824221
 [676]  0.5553699448  0.5337354717  0.9484597815 -0.0400525242  0.0845486659
 [681] -0.7341594939 -0.3150278192  1.8435281527  1.0861525393 -0.2905898712
 [686] -0.1464139496 -0.1620841552  1.6181234455 -2.9809085917 -0.2582210333
 [691]  0.4624996209  1.6421841895 -0.6289817651 -0.2545629242  1.0400713069
 [696]  0.5149184637  0.0077155453 -2.6032632980 -1.0591057168 -0.1274404132
 [701]  0.8387576276  0.6842051812  0.3843689503 -1.9743724307 -0.1459708456
 [706] -1.0479526776  0.2201391273 -0.2412751013  0.2902536278 -1.1281460638
 [711] -0.4988548731 -1.9530590385  0.6315553665 -1.8411795194  0.1715161786
 [716]  0.3974770892  1.2160030699 -0.0335262916 -0.4760830764 -0.2198396411
 [721] -0.8425517054 -0.9635705177  1.4727743537  0.3340560153 -1.4086207539
 [726] -0.6673781266 -0.5047404363 -0.0974504623 -0.4866391339  0.3638134110
 [731]  1.1470103781  1.9540349520  0.8292313638 -1.7354876596  0.5065523398
 [736]  0.1016695331  0.0609132981 -0.4648054180  1.0536399443 -0.3924156871
 [741] -0.0006896923 -0.2158887158  1.1920801582 -1.8488585531  0.5558393823
 [746]  0.3402287820 -1.0824667603  0.8198933645 -0.3221254102 -0.3016422090
 [751]  0.1308765423  1.2350793735 -0.4223497262 -1.2827094225 -0.8716005981
 [756] -1.0764070438 -0.7545846820  0.2145897488 -0.3103965597 -1.0191686079
 [761] -1.2504889432  1.0772671414 -0.8404265526 -0.2385666860  0.8613620599
 [766] -0.4870332109 -1.2172883847  0.2359883478 -0.5278904900  0.0446639552
 [771] -2.0680710854 -1.1407695645 -0.7048544453 -0.5083416310  0.4573689923
 [776]  0.1004436429  0.2104422472  1.2060376660  0.2222813544  1.0430154315
 [781]  0.1214353927  0.6392344157  0.0018168306 -0.4516506267  0.7042120077
 [786] -0.3877704894  0.4392357317  0.5886149100  0.5724879496 -0.7493173295
 [791] -1.1803974134  0.2727801267  0.1282545726  0.2971719736 -0.2672488347
 [796] -1.7628910641 -0.3737163580  0.7237642944 -0.2643428818 -1.2900755883
 [801]  0.4548010233 -0.6500376702 -0.2376851980  0.6587063330 -2.0162007173
 [806] -0.8724687335 -1.1880314126  0.5994980681 -0.6366725465  0.9386189479
 [811]  0.8253431222 -0.6807676546 -2.0660994854 -0.0463747111 -1.7259207392
 [816]  0.6126902543  0.8015261228 -0.2240441464 -0.0010409570  0.7296474834
 [821]  0.6639642593  1.7178264587 -1.0961814862 -0.1253768393  0.4631454834
 [826]  0.4541385542 -0.6917974943 -1.6059852903 -1.2875242778  0.1068569037
 [831] -0.0390878218 -1.4210337356 -0.5535138518  0.4178355334  0.6073241217
 [836] -0.1830596451 -1.1377903547 -0.3726199636  1.3264006425 -2.6257746685
 [841]  0.1018191837 -0.5945605628  0.0165423296  0.5851186156  0.0330005063
 [846] -1.1024835666 -1.2558700103  0.5584590646 -1.4846041925 -0.5313930137
 [851] -0.6877840212  0.6698376299  0.0824739915  0.8284995838  0.3076996943
 [856] -0.1075599307 -0.4829739705 -0.5916408347 -0.6882111815 -0.7497566837
 [861]  1.7126136627 -2.1833326992  0.5230488580  0.9913975809 -1.6251343677
 [866] -0.9791187727  0.4035371068 -0.4010439856 -0.4557556967  0.6965238884
 [871]  0.6344001639 -0.1918209419  2.8619031565 -2.9806569098 -0.4515379702
 [876] -1.5653990289  0.6322802575 -0.1661206402 -0.9409187399 -0.7756365167
 [881]  1.4312926589 -2.6601627048  0.1806129589 -0.2987947129  0.6009392362
 [886] -1.0988494377  0.2396586464 -0.1569129982  1.3793749080 -1.3343787370
 [891] -0.0912332206  0.7447007600 -2.3068794545  1.4955414572  0.1000687734
 [896] -1.9685823201 -0.0630032713 -0.3790359692  0.5382993658  0.1878260782
 [901]  0.5049727081 -1.4052959911 -0.4042643747 -2.5641297997  0.2985031295
 [906]  2.1178722843 -1.7084569851  0.0174355907 -0.6270520408  0.0203961978
 [911] -1.2082789970  0.5876261132  0.4298001804 -0.2857760537  0.6425422825
 [916]  0.1016417281  0.2678264673 -0.8350776622  0.5130021765  1.3835179913
 [921] -1.1562373127 -0.7375360998  1.3929595291  0.4537607306 -1.8729923231
 [926]  1.2994578266  0.2956657150  1.3670240319 -1.3571864380 -0.6040143863
 [931] -0.3642269139  0.5083801273 -0.4817110580 -1.1031368939 -0.5305770366
 [936]  0.1672253429 -1.2610914237 -0.6977508837 -2.3161221967 -0.7645549655
 [941] -0.6177628215  0.7794411102 -0.8243339734 -0.0382117520  0.9235433684
 [946]  1.2860176969 -0.5494503750  1.3180569502  0.3392893151  0.9942623357
 [951] -0.7957322472 -0.6032940683  0.2099423771 -0.3356296879  0.6225337602
 [956] -1.3861685432 -2.3256647508 -1.5028012448  1.6796091315  0.6789906676
 [961] -2.1987683296  0.8547518636  0.5684899831  1.9171139657 -0.2312563939
 [966] -0.2263013183 -0.9990655526  0.6110294079 -0.2925887391  0.3127844554
 [971] -0.2566931133 -0.0792090645  0.0666285920 -0.1506729712  0.1570901136
 [976]  0.5802504448 -0.9643656276  1.1663238648 -0.8135559628 -0.4419462293
 [981]  0.8942601567 -0.5016374459 -0.1587267118  0.3252194405 -0.4731912557
 [986]  3.1474990392  0.0778083456  1.9791082694  0.5086202599 -1.6085858001
 [991]  1.5089047417  0.2054576010  2.0417449651 -1.2008144333  0.5967219827
 [996] -0.2274113766  0.9717461593  0.2080951051 -0.2286184557 -0.1766974791

Random assignment using the Binomial Distribution

Remember, we then randomly assigned them to one of two groups: A or B.

  • I used random draws from the Binomial (read: binary or two) distribution to do this.

Random assignment using the Binomial Distribution

rbinom(n = 1000, size = 1, prob = 0.5)
   [1] 1 1 0 1 1 1 0 0 1 0 1 0 0 0 1 1 0 0 1 0 1 1 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0
  [38] 1 0 1 1 1 0 1 0 0 0 0 1 1 1 1 1 0 1 1 1 0 0 1 1 1 0 0 0 1 0 1 0 1 0 1 0 0
  [75] 1 0 0 1 1 0 0 1 1 1 1 1 1 1 0 1 1 0 1 1 0 0 1 0 1 0 0 0 0 1 1 0 1 0 0 1 0
 [112] 1 1 0 1 0 0 0 0 1 0 1 1 1 1 1 1 1 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0
 [149] 0 0 0 1 1 1 0 0 0 1 1 0 0 1 0 1 1 0 0 1 0 1 1 0 0 1 0 1 0 1 0 1 1 0 1 0 0
 [186] 1 1 1 1 0 0 1 0 0 1 1 1 0 1 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 1
 [223] 1 0 1 0 1 1 1 0 0 1 0 1 0 0 1 0 0 1 1 1 0 0 0 0 0 1 1 1 0 1 1 0 0 0 0 0 0
 [260] 1 1 0 1 1 1 1 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1 0 0 0 1 1 1 1 1 1 1 0 1 0 1 0
 [297] 0 1 1 0 1 1 1 0 0 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 0 0 0 0 0 1 1 1 0 0 1 1 1
 [334] 0 1 1 1 0 1 1 1 1 1 0 0 0 1 0 0 0 0 0 1 0 1 1 0 0 1 1 1 1 0 1 0 0 1 0 0 1
 [371] 0 0 1 1 1 1 0 0 0 1 0 1 0 1 1 0 1 0 0 1 0 1 0 0 1 0 1 1 0 0 1 1 1 1 0 1 0
 [408] 1 1 0 0 1 1 0 1 0 0 1 1 0 0 1 1 1 0 0 1 1 1 0 1 0 0 0 1 1 1 1 0 0 1 0 0 1
 [445] 0 0 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 0 0 1 1 1 1 1
 [482] 0 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 1 0 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0
 [519] 1 1 1 0 0 0 1 0 0 0 0 1 0 1 1 0 0 1 0 0 0 1 0 0 0 0 0 1 1 0 0 0 1 1 0 1 0
 [556] 1 1 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 1 1 0 1 1 1 0 1 1 1 1 1 0 1 0 1 1 0 1 1
 [593] 1 1 0 1 1 0 0 0 1 0 1 1 0 0 0 0 1 1 0 1 0 1 0 1 1 0 1 0 1 0 1 0 0 1 0 1 0
 [630] 1 1 0 0 1 0 1 0 1 1 0 0 1 1 1 1 1 0 0 1 1 0 0 1 0 1 1 1 0 1 0 1 1 0 0 1 1
 [667] 1 1 0 1 0 1 0 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 0 1 1 0 1 1 0
 [704] 0 1 0 0 1 0 0 0 0 1 1 0 0 1 1 1 0 1 1 1 1 0 0 1 0 0 1 1 0 0 1 0 0 0 1 1 1
 [741] 1 0 0 1 1 1 0 1 0 0 1 0 1 1 0 1 0 0 0 0 1 1 1 1 0 0 0 0 1 0 1 0 0 1 1 1 1
 [778] 0 0 0 0 0 1 0 0 1 0 0 1 1 1 0 0 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0 0 1 1 0
 [815] 1 0 1 1 1 1 1 1 0 0 0 1 0 1 1 0 1 0 0 0 0 1 1 0 0 1 1 0 0 0 0 1 0 1 0 1 1
 [852] 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 1 0 0 0 0 1 1 1 1 1 0 1 0 0 0 1 0 1 0 0 0 0
 [889] 1 1 0 1 1 1 0 1 0 1 1 0 1 0 0 1 0 0 1 1 0 1 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0
 [926] 1 1 0 1 0 1 1 0 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 0 1 1
 [963] 1 1 0 1 0 0 1 1 1 0 1 1 1 1 0 0 0 1 0 0 1 1 0 1 1 0 0 0 0 1 0 0 1 0 0 0 1
[1000] 1

The Binomial Distribution

ggplot() + 
  geom_bar(aes(x = rbinom(n = 1e6, size = 1, prob = 0.5))) + 
  theme_minimal()

Assigning our people with mutate()

assigned_group <- group_df |> 
  mutate(
    group = rbinom(1000, 1, 0.5),
    group = factor(group, labels = c("A", "B"))
  )

assigned_group
# A tibble: 1,000 × 5
      id height weight eye_colour group
   <int>  <dbl>  <dbl> <chr>      <fct>
 1     1   170.   76.5 Grey       B    
 2     2   167.   94.4 Grey       B    
 3     3   167.   83.0 Brown      A    
 4     4   175.   80.3 Blue       B    
 5     5   179.   58.4 Blue       B    
 6     6   185.   81.2 Brown      B    
 7     7   167.   77.6 Green      A    
 8     8   171.   74.0 Grey       A    
 9     9   169.   89.0 Brown      B    
10    10   177.  103.  Blue       B    
# ℹ 990 more rows

Comparing our two groups

Comparing our two groups

Comparing our two groups